// ---------------------------------------------------------------------
//
// Copyright (C) 2005 - 2018 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------



// copied from bits/step-11 with slight modifications to make it run faster


#include <deal.II/base/function.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/table_handler.h>

#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/dofs/dof_tools.h>

#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/fe/mapping_q.h>

#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/manifold_lib.h>
#include <deal.II/grid/tria.h>
#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/tria_iterator.h>

#include <deal.II/lac/affine_constraints.h>
#include <deal.II/lac/dynamic_sparsity_pattern.h>
#include <deal.II/lac/precondition.h>
#include <deal.II/lac/solver_cg.h>
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/vector.h>

#include <deal.II/numerics/matrix_tools.h>
#include <deal.II/numerics/vector_tools.h>

#include <algorithm>

using namespace dealii;


template <int dim>
class LaplaceProblem
{
public:
  LaplaceProblem(const unsigned int mapping_degree);
  void
  run();

private:
  void
  setup_system();
  void
  assemble_and_solve();
  void
  solve();

  Triangulation<dim> triangulation;
  FE_Q<dim>          fe;
  DoFHandler<dim>    dof_handler;
  MappingQ<dim>      mapping;

  SparsityPattern           sparsity_pattern;
  SparseMatrix<double>      system_matrix;
  AffineConstraints<double> mean_value_constraints;

  Vector<double> solution;
  Vector<double> system_rhs;

  TableHandler output_table;

  double last_error;
};



template <int dim>
LaplaceProblem<dim>::LaplaceProblem(const unsigned int mapping_degree)
  : fe(1)
  , dof_handler(triangulation)
  , mapping(mapping_degree)
  , last_error(std::numeric_limits<double>::max())
{
  deallog << "Using mapping with degree " << mapping_degree << ":" << std::endl
          << "============================" << std::endl;
}



template <int dim>
void
LaplaceProblem<dim>::setup_system()
{
  dof_handler.distribute_dofs(fe);
  solution.reinit(dof_handler.n_dofs());
  system_rhs.reinit(dof_handler.n_dofs());

  std::vector<bool> boundary_dofs(dof_handler.n_dofs(), false);
  DoFTools::extract_boundary_dofs(dof_handler,
                                  std::vector<bool>(1, true),
                                  boundary_dofs);

  const unsigned int first_boundary_dof =
    std::distance(boundary_dofs.begin(),
                  std::find(boundary_dofs.begin(), boundary_dofs.end(), true));

  mean_value_constraints.clear();
  mean_value_constraints.add_line(first_boundary_dof);
  for (unsigned int i = first_boundary_dof + 1; i < dof_handler.n_dofs(); ++i)
    if (boundary_dofs[i] == true)
      mean_value_constraints.add_entry(first_boundary_dof, i, -1);
  mean_value_constraints.close();

  DynamicSparsityPattern csp(dof_handler.n_dofs(), dof_handler.n_dofs());
  DoFTools::make_sparsity_pattern(dof_handler, csp);
  mean_value_constraints.condense(csp);

  sparsity_pattern.copy_from(csp);
  system_matrix.reinit(sparsity_pattern);
}



template <int dim>
void
LaplaceProblem<dim>::assemble_and_solve()
{
  const unsigned int gauss_degree =
    std::max(static_cast<unsigned int>(
               std::ceil(1. * (mapping.get_degree() + 1) / 2)),
             2U);
  MatrixTools::create_laplace_matrix(mapping,
                                     dof_handler,
                                     QGauss<dim>(gauss_degree),
                                     system_matrix);
  VectorTools::create_right_hand_side(mapping,
                                      dof_handler,
                                      QGauss<dim>(gauss_degree),
                                      Functions::ConstantFunction<dim>(-2),
                                      system_rhs);
  Vector<double> tmp(system_rhs.size());
  VectorTools::create_boundary_right_hand_side(mapping,
                                               dof_handler,
                                               QGauss<dim - 1>(gauss_degree),
                                               Functions::ConstantFunction<dim>(
                                                 1),
                                               tmp);
  system_rhs += tmp;

  mean_value_constraints.condense(system_matrix);
  mean_value_constraints.condense(system_rhs);

  solve();
  mean_value_constraints.distribute(solution);

  Vector<float> norm_per_cell(triangulation.n_active_cells());
  VectorTools::integrate_difference(mapping,
                                    dof_handler,
                                    solution,
                                    Functions::ZeroFunction<dim>(),
                                    norm_per_cell,
                                    QGauss<dim>(gauss_degree + 1),
                                    VectorTools::H1_seminorm);
  const double norm = norm_per_cell.l2_norm();

  output_table.add_value("cells", triangulation.n_active_cells());
  output_table.add_value("|u|_1", norm);
  output_table.add_value("error",
                         std::fabs(norm - std::sqrt(3.14159265358 / 2)));

  last_error = std::fabs(norm - std::sqrt(3.14159265358 / 2));
}



template <int dim>
void
LaplaceProblem<dim>::solve()
{
  SolverControl solver_control(1000, 1e-12);
  SolverCG<>    cg(solver_control);

  PreconditionSSOR<> preconditioner;
  preconditioner.initialize(system_matrix, 1.2);

  cg.solve(system_matrix, solution, system_rhs, preconditioner);
}



template <int dim>
void
LaplaceProblem<dim>::run()
{
  GridGenerator::hyper_ball(triangulation);
  static const SphericalManifold<dim> boundary;
  triangulation.set_manifold(0, boundary);

  for (unsigned int cycle = 0; cycle < 6;
       ++cycle, triangulation.refine_global(1))
    {
      setup_system();
      assemble_and_solve();
    };

  AssertThrow(last_error < 1e-3, ExcMessage("solution is not converging"));



  output_table.set_precision("|u|_1", 6);
  output_table.set_precision("error", 6);
  output_table.write_text(std::cout);
  deallog << std::endl;
}



int
main()
{
  try
    {
      LaplaceProblem<2>(1).run();
    }
  catch (std::exception &exc)
    {
      deallog << std::endl
              << std::endl
              << "----------------------------------------------------"
              << std::endl;
      deallog << "Exception on processing: " << std::endl
              << exc.what() << std::endl
              << "Aborting!" << std::endl
              << "----------------------------------------------------"
              << std::endl;
      return -1;
    }
  catch (...)
    {
      deallog << std::endl
              << std::endl
              << "----------------------------------------------------"
              << std::endl;
      deallog << "Unknown exception!" << std::endl
              << "Aborting!" << std::endl
              << "----------------------------------------------------"
              << std::endl;
      return -1;
    };

  return 0;
}
